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Search: id:A160414
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| A160414 |
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Same as A160410, except start with one ON cell, not four. |
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+0
14
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| 0, 1, 9, 21, 49, 61, 97, 133, 225, 237, 273, 309, 417, 453, 561, 669, 961
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Has a fractal-like behavior similar to the toothpick sequence A139250.
First differences: A161415, where there is an explicit formula for the n-th term.
Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton. [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
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LINKS
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O. E. Pol, Illustration of initial terms [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
Index entries for sequences related to cellular automata [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
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EXAMPLE
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If we label the generations of cells turned ON by consecutive numbers we get the cell pattern shown below:
99.............99
98888888888888889
.877887787788778.
.876666787666678.
.886556888655688.
.886544444445688.
.876643343346678.
.877843222348778.
.888844212448888.
.877843222348778.
.876643343346678.
.886544444445688.
.886556888655688.
.876666787666678.
.877887787788778.
98888888888888889
99.............99
In the first generation, only the central "1" is ON, a(1)=1. In the next generation, we turn ON eight "2"'s around the central cell, leading to a(2)=a(1)+8=9. In the third generation, twelve "3"'s are turned ON around the vertices of the square, a(3)=a(2)+3*4=21, and so on.
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CROSSREFS
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Cf. A139250, A139251, A160118, A160410, A160412.
Cf. A000079, A000225, A060867, A160117, A161415, A160720, A160727, A151725.
Sequence in context: A020190 A135187 A133762 this_sequence A118130 A144482 A134717
Adjacent sequences: A160411 A160412 A160413 this_sequence A160415 A160416 A160417
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KEYWORD
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more,nonn,new
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), May 20 2009, Jun 13 2009, Jun 14 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Jun 15 2009 and Jul 13 2009
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